MICHIGAN ACADEMY OP SCIENCE. 



105 



Legs I — II. Mean coefficient (homologous joints) — mean coefficient (non-homologus joints) = .9402 — 



.9309 = .0093±.0135. 

 Legs II — III. Mean coefficient Oiomologous joints) — mean coefficient (non-liomologous joints)= 



.9420— .9140 (=) .0280±.0196. 

 Legs I — III. Mean coefficient (liomologous joints) — mean coefficient (non-homo!gous joints)=.9280 — 



. 9264 = . 0016±. 0207. 



In each case the mean coefficient for the non-homologous joints is smaller than that 

 for the homologous. In the case of the Legs I-II and Legs II-III the difference between 

 mean coefficients of homolgous and non-homologous joints is less than the probable er- 

 ror of the difference,^ and with the Legs II-III the difference is but little more than 

 the probable error. It would seem then that the differences are not significant. 



Taking the mean of the means of the three leg pairs we get as a general average for the 

 correlation between homologous joints in the three legs a coefficient of .9367 ±.0085. The 

 general average for the non-homologous joints is .9238 ±.0063. The difference between 

 the two is then .0128 with a probable error of ^.0106. It would thus appear that the 

 homologous and non-homologous joints of the legs of the crayfish are correlated to sen- 

 sibly the same degree. 



In order to analyze the data somewhat more closely it seemed desirable to consider each 

 joint separately. This has been done in Tables II, III, and IV. 



TABLE II. 



Meripodite Correlation. 



A. HOMOLOGOUS JOINTS. 



B.NOX-HOMOLOGOUS JOINTS. 



Joints. 



Meripodite-carpopodite. 

 Carpopodite-meripodite 

 Meripodite-propodite. . . 

 Propodite-meripodite. . 

 Mean 



Legs I— II. 



. 9808 ± .0083 

 .9502± .0039 

 .9578± .0033 

 .9440± .0044 

 .9357 



Legs II— III. 



.8632+ .0102 

 .9185+ .0063 

 .9626+ .0030 

 .9670+ .0026 

 .9278 



Legs I— III. 



.8652+ .0101 

 .9601 + .0031 

 .9646± .0028 

 .9539+ .0036 

 .9359 



From Table II the general average coefficient for the correlation of meripodite with 

 meripodite for the three pairs is .9693:^^.0010. For the non-homologous joint pairs in 

 which a meripodite enters as one variable the general average coefficient is .9332 ±.0015. 

 The difference then is .0361:^^.0018, the homologous joints showing the higher correlation. 



The considerable difference in average correlation shown in this table is to be explained 

 in part as a result of the inclusion in the B group of the pairs of joints containing as one 

 member a carpopodite. It has appeared throughout the work that there is a general 

 tendency for carpopodite correlations to run relatively low. This being the case it is evi- 

 dent that if we include in one half of a table several such pairs of joints which generally 

 exhibit a relatively low correlation and exclude any such pairs from the other half, we 

 should expect to get a significant difference between the average coefficients for the two 

 halves. This is exactly what occurs in the table. 



TABLE III. 

 Carpopodite Correlation. 



A. HOMOLOGOUS JOINTS. 



lit sliould be stated that the probable errors of the mean coefficient deduced from the tables were 

 calculated by the ordinary formula for the probable error of a mean, viz., P. E. means=. 67449 a. 

 In obtaining or each coefficient was given equal weight or in other words a frequency of 1 . 



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